Final answer:
To find the z-scores for left-tail probabilities of 0.9947 and 0.7675 on a standard normal distribution, one would use a z-table or calculator function such as invNorm to determine the corresponding z-scores for the probabilities provided.
Step-by-step explanation:
The question relates to finding the z-score for a given left-tail probability on a standard normal distribution. The z-score corresponds to how many standard deviations away from the mean a point is on this distribution. For a left-tail probability of 0.9947, one would use a z-table or calculator to find the z-score that has 99.47% of the area under the curve to its left. For a probability of 0.7675, the procedure is similar; locate the z-score that corresponds to 76.75% of the area under the curve to its left.
To find the z-score corresponding to the left-tail probability of 0.9947, we can use a probability table for the standard normal distribution or software/calculator with the function invNorm(0.9947). Similarly, to find the z-score for a left-tail probability of 0.7675, use the function invNorm(0.7675).
These z-scores are used to determine how an individual score relates to the distribution as a whole. They can be used for calculating probabilities, determining percentiles, and testing hypotheses in statistics.